DESIGN OF MACHINERY SOLUTION MANUAL 8-8- 1 PROBLEM 8-8 S tat ement: Desig n a double- dwell c am to mov e a follower from 0 to 1 .5 in in 45 deg , dwell f or 150 deg , fall 1. 5 i in 90 deg and dwell for the rema inder. The total cy cle must take 6 sec. Choose suita ble progr ams for rise and fall to minimize velocities. Plot the SVAJ diagrams. Given: RISE DWELL FALL DWELL 1 45 deg 2 150 deg 3 90 d eg 4 75 deg h 1 1.5 in h 2 0 in h 3 1.5 in h 4 0 in Cycle time: 6 sec S olution: See Mathcad file P0808. 1. The camshaf t turn s 2 rad during the time for one cy cle. Thus, its spee d is 2 rad 1.047 rad sec 2. The modi fied sinu soidal mot ion is defi ned in loca l coordin ates by equation s 8.15 thro ugh 8.19 . The nume rical constants in these SCCA equations are given in Table 8-2. b 0.25 c 0.00 d 0.75 C a 5.5280 3. The SC CA eq uations for th e rise or fal l inter val ( ) are div ided into 5 su binterv als. These ar e: for 0 <= x <= b /2 where , for these equatio ns, x is a local coordinate that ranges from 0 to 1 y 1 x ( ) C a x b b 2 sin b x y' 1 x ( ) C a b 1 cos b x y'' 1 x ( ) C a sin b x y''' 1 x ( ) C a b cos b x for b/2 <= x <= (1 - d )/2 y 2 x ( ) C a x 2 2 b 1 1 2 x b 2 1 8 1 2 y' 2 x ( ) C a x b 1 1 2 y'' 2 x ( ) C a y''' 2 x ( ) 0 for (1 - d )/2 <= x <= (1 + d )/2 y 3 x ( ) C a b c 2 x d 2 b 2 1 8 1 2 1 d ( ) 2 8 d 2 cos d x 1 d 2 y' 3 x ( ) C a b c 2 d sin d x 1 d 2 y'' 3 x ( ) C a cos d x 1 d 2 y''' 3 x ( ) C a d sin d x 1 d 2